bre02177_app11A_001-009.indd Page 1 11/23/10 8:31 AM user-f494
Appendix 11A
/207/MHRL046/bre02177_disk1of1/0070002177/bre02177_pagefiles
Multi-product Break-Even Analysis
Before concluding our discussion, we should consider one additional application of the ideas that we have developed—the use of CVP (cost-volume-profit) concepts in multiproduct/multi-service settings. One concept that is critical in such a setting is that of sales mix which is discussed below.
The Definition of Sales Mix The term sales mix refers to the relative proportions in which a company’s products/ services are sold. Managers try to achieve the combination, or mix, that will yield the greatest amount of profits. Most companies have many products, and often these products are not equally profitable. In these companies, profits will depend to some extent on the company’s sales mix. Profits will be greater if high-margin, rather than low-margin, items make up a relatively large proportion of total sales. Once again the concept of contribution margin is the key. In a multiple product setting, managers who focus solely on increasing the total sales volume in an effort to improve the profitability of their companies can cause the profits to decline. On the one hand, if the increase in volume was obtained by shifting the sales mix from high-margin items to low-margin items, then total profits will decrease. On the other hand, if a shift in sales mix from low-margin items to high-margin items occurs, total profits can increase, even though total sales may decrease. It is one thing to achieve a particular sales volume; it is quite a different thing to sell the most profitable mix of products. Whether an organization’s sales force will focus on achieving volume or profitability will partially depend on their incentive systems.
KNOW CC14A: Explain the concept of sales mix.
Sales Mix and Break-Even Analysis If a company sells more than one product, break-even analysis is somewhat more complex than our previous coverage shown in Chapter 11. The reason is that different products will have different selling prices, different costs, and different contribution margins. To illustrate, consider Sound Unlimited, a small company that imports DVD-ROM drives from France for use in personal computers. At present, the company distributes three models of DVD-ROM drives to retail computer stores: Le Louvre, Le Vin, and Le Rouge. Planned sales, expenses, income, and break-even sales for the month of September are shown in Exhibit 11A–1. The planned sales mix for the month is 2:3:5, that is, the sales ratio is 20% for Le Louvre, 30% for Le Vin, and 50% for Le Rouge adding up to 100%.1 Note that the contribution margin for each model is different: 30% for Le Louvre, 20% for Le Vin and
APPLY CC15A: Compute break-even sales in a multi-product environment.
1 Here we have calculated the sales mix ratio using sales revenues as the basis; it can also be computed using sales in units as the basis for calculation. It is important to note that the sales mix ratios of individual products calculated using sales revenues and sales in units will not be the same because sales revenue is a function of sales in units and sales price.
1
3rd Pass
$ 32,000
$ 4,500
20.0%
100.0% 80.0
$15,000
$37,500 22,500
40.0%
$24,000
$75,000 51,000
0
$
30.0%
$22,500 18,000
100.0% $75,000
100.0%
8,000
Net income . . . . . . . . . . . . . . . . . . . . . . . . . . .
$ 4,500
Contribution margin . . . . . . . . . . . . . . . . . . . .
100.0% 70.0
50.0% $37,500 100.0% 60.0
40.0%
$100,000 68,000
24,000
$15,000 10,500
Break-Even Income Statement Break-even sales . . . . . . . . . . . . . . . . . . . . . . . Less: Variable expenses . . . . . . . . . . . . . . . . . .
30.0% $22,500
$75,000
50.0% 5 40.0%
$20,000
100.0% 60.0
Less: Fixed expenses . . . . . . . . . . . . . . . . . . . .
20.0% $15,000
Break-Even Sales by Product Break-even sales ratio . . . . . . . . . . . . . . . . . . . Break-even sales by product . . . . . . . . . . . . . .
Overall break-even sales . . . . . . . . . . . . . . . . .
Sales Ratio and Overall Break-Even Sales Sales ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sales mix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contribution margin ratio . . . . . . . . . . . . . . . . Weighted-average contribution margin ratio . . 20.0% : 30.0% : 2 : 3 : 30.0% 20.0% 32.0% (20% 3 30% 1 30% 3 20% 1 50% 3 40%) Fixed expenses, $24,000 5 Weighted-average contribution margin ratio, 32%
20.0%
$50,000 30,000
$
$ 6,000
100.0% 80.0
Net income . . . . . . . . . . . . . . . . . . . . . . . . . . .
30.0%
$30,000 24,000
Total Amount
$ 24,000
$ 6,000
Contribution margin . . . . . . . . . . . . . . . . . . . .
100.0% 70.0
Percent
Le Rouge Amount
Less: Fixed expenses . . . . . . . . . . . . . . . . . . . .
$20,000 14,000
Percent
Le Vin Amount
32.0%
100.0% 68.0
32.0%
100.0% 68.0
Percent
2
Planned Sales and Income Sales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Less: Variable expenses . . . . . . . . . . . . . . . . . .
Percent
Le Louvre
SOUND UNLIMITED MULTI-PRODUCT BREAK-EVEN SALES ANALYSIS For the Month of September
Amount
Multi-product Break-Even Analysis (Planned)
Exhibit 11A–1
bre02177_app11A_001-009.indd Page 2 11/23/10 8:31 AM user-f494 /207/MHRL046/bre02177_disk1of1/0070002177/bre02177_pagefiles
Appendix 11A
3rd Pass
$ 28,500
$ 8,421
20.0%
100.0% 80.0
$11,789
$29,474 17,684
40.0%
$24,001
$84,211 60,210
1
$
30.0%
$42,105 33,684
100.0% $84,211
100.0%
4,500
Net income . . . . . . . . . . . . . . . . . . . . . . . . . . .
$ 3,789
Contribution margin . . . . . . . . . . . . . . . . . . . .
100.0% 70.0
35.0% $29,474 100.0% 60.0
40.0%
$100,000 71,500
24,000
$12,632 8,842
Break-Even Income Statement Break-even sales . . . . . . . . . . . . . . . . . . . . . . . Less: Variable expenses . . . . . . . . . . . . . . . . . .
50.0% $42,105
$84,211
35.0% 5 40.0%
$14,000
100.0% 60.0
Less: Fixed expenses . . . . . . . . . . . . . . . . . . . .
15.0% $12,632
Break-Even Sales by Product Break-even sales ratio . . . . . . . . . . . . . . . . . . . Break-even sales by product . . . . . . . . . . . . . .
Overall break-even sales . . . . . . . . . . . . . . . . .
Sales Ratio and Overall Break-Even Sales Sales ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sales mix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contribution margin ratio . . . . . . . . . . . . . . . . Weighted-average contribution margin ratio . . 15.0% : 50.0% : 2 : 3 : 30.0% 20.0% 28.5% (15% 3 30% 1 50% 3 20% 1 35% 3 40%) Fixed expenses, $24,000 5 Weighted-average contribution margin ratio, 28.5%
20.0%
$35,000 21,000
Total Amount
$
$ 10,000
100.0% 80.0
Percent
Le Rouge Amount
Net income . . . . . . . . . . . . . . . . . . . . . . . . . . .
30.0%
$50,000 40,000
Percent
Le Vin Amount
$ 24,000
$ 4,500
Contribution margin . . . . . . . . . . . . . . . . . . . .
100.0% 70.0
Percent
Less: Fixed expenses . . . . . . . . . . . . . . . . . . . .
$15,000 10,500
Amount
Le Louvre
SOUND UNLIMITED MULTI-PRODUCT BREAK-EVEN SALES ANALYSIS For the Month of September
Planned Sales and Income Sales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Less: Variable expenses . . . . . . . . . . . . . . . . . .
Multi-product Break-Even Analysis (Actual)
Exhibit 11A–2
28.5%
100.0% 71.5
28.5%
100.0% 71.5
Percent
bre02177_app11A_001-009.indd Page 3 11/23/10 8:31 AM user-f494 /207/MHRL046/bre02177_disk1of1/0070002177/bre02177_pagefiles
Multi-product Break-Even Analysis 3
3rd Pass
bre02177_app11A_001-009.indd Page 4 11/23/10 8:31 AM user-f494
4
/207/MHRL046/bre02177_disk1of1/0070002177/bre02177_pagefiles
Appendix 11A
40% for Le Rouge. Using the sales mix (sales ratio) and the individual contribution ratios, we can compute the weighted-average contribution ratio, as follows: Weighted-average contribution margin ratio 5 (20% 3 30%) 1 (30% 3 20%) 1 (50% 3 40%) 5 6% 1 6% 1 20% 5 32% As is shown in Exhibit 11A–1, the break-even sales for the company is $75,000; this is computed by dividing the fixed expenses of $24,000 by the weighted-average contribution margin ratio of 32%. Using the planned sales mix, we can compute the break-even sales for the three DVD-ROM models as follows: Le Louvre . . . . . 20% of $75,000 5 $15,000 Le Vin . . . . . . . . 30% of $75,000 5 $22,500 Le Rouge . . . . . 50% of $75,000 5 $37,500 The sales of $75,000 represents the break-even level only as long as the sales mix does not change. If the sales mix changes, the break-even sales will change. This is illustrated in Exhibit 11A–2, which shows the actual sales for September. As is shown in Exhibit 11A–2, the sales mix shifted away from the highest contribution margin product (Le Rouge) to the lowest contribution margin (Le Vin). Although total sales remained unchanged at $100,000, net income dropped from the planned $8,000 to $4,500 due to the shift in the sales mix—a decrease of $3,500 (over 43%). Moreover, the weighted-average contribution margin ratio dropped from the planned 32% to 28.5%, resulting in a higher break-even sales of $84,211 in contrast to the planned $75,000 (an increase of over 12%). In performing the break-even analysis, you have to make certain key assumptions as discussed in the chapter. However, if the manager senses changes in the market conditions, as well as the internal environment, that might require a change in the sales mix or the contribution margin ratio, he or she must revise her assumptions, redo the analysis, and use the new results for purposes of planning and decision making.
Application Competency Summary for Appendix 11A Application Competency
Deliverable
Compute breakeven sales in a multi-product situation.
Key Information Sales required to incur no profit and no loss
CC15A
Report/Document No specific report
Source Documents and Key Information Sales, Cost/Expense Accounts in the General Ledger Actual sales, variable and fixed costs Master Budget Budgeted sales, variable and fixed costs (for budgeted reports)
Steps 1. Determine the sales mix, and use it to compute the weightedaverage contribution margin per unit or contribution margin ratio.
Knowledge Competency Contribution margin ratio Sales mix
2. Divide the fixed expenses by the weighted-average contribution margin per unit (ratio) to compute the break-even sales in units (dollars). 3. Determine break-even sales for individual products in the same ratio as the sales mix.
3rd Pass
bre02177_app11A_001-009.indd Page 5 11/23/10 8:31 AM user-f494
/207/MHRL046/bre02177_disk1of1/0070002177/bre02177_pagefiles
Multi-product Break-Even Analysis
5
Questions for Appendix 11A 11–11 What is meant by the term sales mix? What assumption is usually made concerning sales mix in CVP analysis? 11–12 Explain how a shift in the sales mix could result in both a higher break-even point and a lower net income.
Brief Exercises for Appendix 11A BRIEF EXERCISE 11–13 Compute the Break-Even Point for a Multi-product Company (CC14A, 15A) Lucido Products markets two computer games: Claimjumper and Makeover. A contribution margin income statement for a recent month for the two games appears as follows: Claimjumper
Makeover
Total
Sales . . . . . . . . . . . . . . . . . . . . . . . . Less: Variable expenses . . . . . . . . . .
$65,000 45,000
$85,000 60,000
$150,000 105,000
Contribution margin . . . . . . . . . . . .
$20,000
$25,000
45,000
Less: Fixed expenses . . . . . . . . . . . .
36,000
Net income . . . . . . . . . . . . . . . . . . .
$
9,000
Required: 1. Compute the overall CM ratio for the company. 2. Compute the overall break-even point for the company in sales dollars. 3. Verify the overall break-even point for the company by constructing an income statement showing the appropriate levels of sales for the two products. BRIEF EXERCISE 11–14 Break-Even Analysis (CC15A) Jose Co. produces two products, X and Y. The following information is presented for the two products:
Selling price per unit . . . . . . . Variable cost per unit. . . . . . .
X
Y
$9 7
$6 3
Total fixed costs are $117,000. Required: What will the break-even point be for Jose in units of X and Y if the ratio of sales is expected to be 3:1? (Adapted © CGA-Canada) BRIEF EXERCISE 11–15 Contribution Margin Analysis (CC1, 15A) Jeffries Ltd. has two divisions, Andrew and Baldwin. Jeffries’ overall CM ratio is 30%, and combined sales in the two divisions total $500,000. Required: If variable expenses in Andrew are $300,000 and Andrew’s contribution margin ratio is 25%, what are sales in Baldwin? (Adapted © CGA-Canada) BRIEF EXERCISE 11–16 Weighted-Average Contribution Margin Ratio (CC15A) Abernathy Inc.’s sales mix ratio for its four products are 15%, 25%, 20%, and 40%. The respective contribution margins are 25%, 35%, 20%, and 30%. Required: What is the weighted-average contribution margin ratio of the sales mix? (Adapted © CGA-Canada)
3rd Pass
bre02177_app11A_001-009.indd Page 6 11/23/10 8:31 AM user-f494
6
/207/MHRL046/bre02177_disk1of1/0070002177/bre02177_pagefiles
Appendix 11A
Exercise for Appendix 11A EXERCISE 11–13 Multi-product Break-Even Analysis (CC15A) Olongapo Sports Corporation is the distributor in the Philippines of two premium golf balls—the Flight Dynamic and the Sure Shot. Monthly sales and the contribution margin ratios for the two products follow (the currency in the Philippines is the peso, denoted by P): Sales . . . . . . . . . CM ratio . . . . . .
P300,000 70%
P500,000 46%
P800,000 ?
Fixed expenses total P327,500 per month. Required: 1. Prepare an income statement for the company as a whole. Carry computations to one decimal place. 2. Compute the break-even point for the company based on the current sales mix. 3. If total sales increase by P150,000 a month, by how much would you expect net income to increase? What are your assumptions?
Problems for Appendix 11A CHECK FIGURE (2) Break-even: ak-even: B| 1,72 1,728,000
PROBLEM 11–11 Sales Mix; Multi-product Break-Even Analysis (CC1, 15A) Gold Star Rice, Ltd., of Thailand, exports Thai rice throughout Asia. The company grows three varieties of rice—Fragrant, White, and Loonzain. Budgeted sales by product and in total for the coming month are shown following (the currency in Thailand is the baht, denoted by B| ):
Product White
Fragrant
Loonzain
Total
Percentage of total sales . . . . . . . . . Sales. . . . . . . . . . . . . . . . . . . . . . . . . Less: Variable expenses . . . . . . . . . .
20 B| 300,000 216,000
100 72
52 B| 780,000 156,000
100 20
28 B| 420,000 168,000
100 40
100 B| 1,500,000 540,000
100 36
Contribution margin . . . . . . . . . . . .
B| 84,000
28
B| 624,000
80
B| 252,000
60
960,000
64
Less: Fixed expenses . . . . . . . . . . . .
898,560 B|
Net income . . . . . . . . . . . . . . . . . . .
Break-even sales:
61,440
Fixed expenses, B| 898,560 5 B| 1,404,000 CM ratio, 0.64
As shown by these data, net income is budgeted at B| 61,440 for the month and break-even sales at B| 1,404,000. Assume that actual sales for the month total B| 1,500,000 as planned. Actual sales by product are: White, B| 600,000; Fragrant, B| 360,000; and Loonzain, B| 540,000. Required: 1. Prepare a contribution margin income statement for the month on the basis of actual sales data. Present the income statement in the format shown above. 2. Compute the break-even sales for the month on the basis of your actual data. 3. Considering the fact that the company met its B| 1,500,000 sales budget for the month, the president is shocked at the results shown on your income statement in part (1). Prepare a brief memo for the president explaining why both the operating results and break-even sales are different from what was budgeted.
3rd Pass
bre02177_app11A_001-009.indd Page 7 11/23/10 8:31 AM user-f494
/207/MHRL046/bre02177_disk1of1/0070002177/bre02177_pagefiles
Multi-product Break-Even Analysis
PROBLEM 11–12 Multi-product Break-Even and Target Profit Analysis (CC9, 15A) Fashonista Inc. has created a new type of sandal that is expected to be popular with active people. It comes in two models—the Farideh and the Mercury. Cost and production data are as follows:
Selling price. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cost to produce 50,000 units of each product: Direct materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . Direct labour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variable overhead . . . . . . . . . . . . . . . . . . . . . . . . . . Fixed overhead allocation . . . . . . . . . . . . . . . . . . . . Selling and administrative costs: Shipping costs per unit . . . . . . . . . . . . . . . . . . . . . . Advertising budget allocated . . . . . . . . . . . . . . . . . .
Farideh
Mercury
$29.99
$49.99
$350,000 75,000 500,000 356,000
$400,000 75,000 550,000 400,000
$ 1.99 100,000
$ 1.99 150,000
7
CHECK FIGURE (1) 48,000 units
Required: 1. Calculate the break-even point in units for the Farideh model, assuming the allocations of fixed costs given above. 2. Total unit sales are budgeted at 100,000 units, the allocated fixed overhead amounts are as given, and the Farideh model is expected to account for 70% of unit sales and the Mercury model 30%. Calculate the break-even sales level in dollars for the products combined. 3. What is the break-even sales level in dollars for the combined products if the fixed overhead were allocated to the two models in proportion to their sales—that is, 70% of fixed overhead allocated to Farideh and 30% of fixed overhead allocated to Mercury? Briefly explain your response. (Adapted © CGA-Canada) PROBLEM 11–13 Sales Mix; Break-Even Analysis; Margin of Safety (CC12, 14A, 15A) Island Novelties, Inc. of Palau makes two products—Hawaiian Fantasy and Tahitian Joy. Present revenue, cost, and sales data on the two products follow: Hawaiian Fantasy Selling price per unit . . . . . . . . . . . . . . . . . . $ 45 Variable expenses per unit . . . . . . . . . . . . . . 27 Number of units sold annually. . . . . . . . . . . 20,000
CHECK FIGURE (1b) Break-even: $2,196,000 (2b) Margin g of safety: 22%
Tahitian Joy $ 300 60 5,000
Fixed expenses total $1,427,400 per year. The Republic of Palau uses the U.S. dollar as its currency. Required: 1. Assuming the sales mix given above, do the following: a. Prepare a contribution margin income statement as in Chapter 11, showing both dollar and percent columns for each product and for the company as a whole. b. Compute the break-even point in dollars for the company as a whole and the margin of safety in both dollars and as a percentage. 2. Another product, Samoan Delight, has just come on the market. Assume that the company could sell 10,000 units at $135 each. The variable expenses would be $108 each. The company’s fixed expenses would not change. a. Prepare another contribution margin income statement, including sales of Samoan Delight (sales of the other two products would not change). Carry percentage computations to one decimal place. b. Compute the company’s new break-even point in dollars and the new margin of safety in both dollars and percent. 3. The president of the company examines your figures and says, “There’s something strange here. Our fixed costs haven’t changed, and you show greater total contribution margin if we add the new product, but you also show our break-even point going up. With greater contribution margin, the break-even point should go down, not up. You’ve made a mistake somewhere.” Explain to the president what has happened.
3rd Pass
bre02177_app11A_001-009.indd Page 8 11/23/10 8:31 AM user-f494
8
CHECK FIGURE (1a) $42,695
/207/MHRL046/bre02177_disk1of1/0070002177/bre02177_pagefiles
Appendix 11A
PROBLEM 11–14 Multi-product Break-Even Analysis (CC15A) Mitchell Co. Ltd. manufactures three lines of tires—models I, II, and III. The three different models sell for the same price, but they use different rubber compounds and have slightly different manufacturing processes. Note: All data are in thousands, unless stated otherwise.
Budget, May 2008
Model I Model II Model III Total
Units
Sales
Variable Costs
Contribution
875 250 350
$ 43,750 52,500 61,250
$ 25,375 31,500 22,050
$ 18,375 21,000 39,200
1,475
$157,500
$ 78,925
$ 78,575
Fixed costs for the combined sales are $21.3 million per month. During May, selling prices, variable costs per unit, and fixed costs were according to budget. However, the actual units sold were the following: Model I Model II Model III
725 450 300 1,475
Required: 1. Calculate the break-even volume for the month of May for: a. The budgeted mix of products b. The actual mix of products sold (Adapted © CGA-Canada)
CHECK FIGURE (2) 65,229 (rounded up)
PROBLEM 11–15 Multi-product Break-Even Analysis (CC15A) OnTime Inc. produces two lines of clocks—standard and deluxe. Cost and revenue data are shown, as follows:
Selling price (per clock): Variable costs (per clock) . . . . . . . . . . . . . . . . . . . . Direct materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . Direct labour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Overhead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Selling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contribution margin (per clock) . . . . . . . . . . . . . . . . . Sales mix (% of total sales in units) . . . . . . . . . . . . . . Total contribution margin . . . . . . . . . . . . . . . . . . . . . .
$1,184,000
Fixed manufacturing costs (total for both lines of clocks) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Administrative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Net income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
450,000 305,000 $ 384,000
Total expected sales in units (the two lines of clocks combined). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Capacity (the two lines of clocks combined) . . . . . . .
80,000 100,000
Standard
Deluxe
$
$
40
10 12 4 2 $ 12 60% $576,000
60
18 16 5 2 $ 19 40% $608,000
3rd Pass
bre02177_app11A_001-009.indd Page 9 11/23/10 8:31 AM user-f494
/207/MHRL046/bre02177_disk1of1/0070002177/bre02177_pagefiles
Multi-product Break-Even Analysis
9
Required: The following three cases are independent but are based on the preceding data. 1. The company is considering steps to increase sales, particularly of the deluxe model. It is considering increasing advertising by $200,000 and increasing the sales commission on the deluxe clock by $2 per clock. Management believes that these steps will increase total sales to 95,000 clocks and increase the proportion of deluxe models sold to 50%. Calculate the new net income if both changes were implemented and the resulting sales were as predicted. 2. The management of OnTime is considering purchasing new equipment that will reduce direct materials and direct labour costs by 20% for both products. The new equipment would increase fixed manufacturing costs by $175,000, reflecting the amortization on the new equipment. Calculate the total sales volume (in units) that must be achieved in order for the purchase of the new equipment to have a positive effect on net income. Assume that the sales mix would be unaffected. (Adapted © CGA-Canada)
3rd Pass
